A coil 4.00 cm radius, containing 550 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 3.00×10−5 T/s4 )t4. The coil is connected to a 510-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.What is the current in the resistor at time t0 = 5.10 s
given
r = 4 cm = 0.04 m
N = 550 turns
B = 1.2*10^-2 t + 3*10^-5*t^4
dB/dt = 1.2*10^-2 + 3*10^-5*4*t^3
= 1.2*10^-2 + 1.2*10^-4*t^3
induced emf in the coil,
emf = N*A*dB/dt
= 550*pi*0.04^2*(1.2*10^-2 + 1.2*10^-4*t^3 )
at t = 5.1 s
emf = 550*pi*0.04^2*(1.2*10^-2 + 1.2*10^-4*5.1^3 )
= 0.07718 V
induced current = induced emf/R
= 0.07718/510
= 1.51*10^-4 A <<<<<<<<<<<-----------------Answer
A coil 4.00 cm radius, containing 550 turns, is placed in a uniform magnetic field that...
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